The course provides introductory material on general relativity and its mathematical language of differential geometry. This is followed by more advanced modules with applications to the study of black holes, cosmology and aspects of general relativity related to string theory. There is a year-long introduction to quantum field theory which introduces the famous Feynman diagrams of particle physics in a systematic way, and studies aspects of modern particle physics. There is also an introduction to the concepts of quantum information theory.
The course assumes students have a familiarity with quantum mechanics and special relativity at an introductory level. No prior knowledge of general relativity is assumed.
Taken full-time, the course lasts a full year, starting in September.
The course has a simple structure, consisting of 180 credits, split into 120 credits of taught modules during the autumn and spring semesters and a 60-credit research project that is completed in the summer period. All modules are compulsory.
Modules are mainly delivered through lectures and example and/or problem classes. You will typically be assessed by an examination at the end of the semester in which a given module is taught. However a small proportion of the assessment is by coursework, essay and student presentation.
During the summer period, you will concentrate on an independent maths research project under the supervision of a member of academic staff, writing a substantial dissertation.
Here are a few maths books that can be used to brush up on prerequisite material.
- Classical Mechanics by Kibble and Berkshire (In particular, it is worth looking at Lagrangian and Hamiltonian mechanics in Ch10, 11 and 12).
- Quantum Mechanics Demystified by David McMahon
- Flat and curved space-times by George F. Ellis and Ruth M. Williams (The first part covers special relativity and the second part will be useful for the MSc course).
- Mathematical Methods for Physics and Engineering: A Comprehensive Guide by K. F. Riley, M. P. Hobson, S. J. Bence (the key topics are vector calculus/analysis, Fourier series and Fourier transforms, the Laplace equation, the heat equation, the wave equation, complex variables and contour integration).
For the modules taught during the MSc, here are a few suggestions for preliminary reading that will introduce some of the ideas in a fairly non-technical way. These aren't supposed to cover all the module material but are there just to get you started.
- General Relativity, black holes and cosmology: Flat and curved space-times by George F. Ellis and Ruth M. Williams.
- Gravity: An Introduction to Einstein's General Relativity by J.B. Hartle.
- Quantum Field Theory: Quantum Field Theory in a Nutshell by A. Zee. This book has a very good discussion of the concepts but does get to quite advanced topics (some of which are not in the MSc).
- QED The Strange Theory of Light and Matter, by R.P. Feynman.
Students successfully completing the course should have demonstrated:
- Knowledge and understanding of a range of mathematical core concepts and results in gravitation and quantum theory.
- Knowledge and understanding of some advanced concepts and techniques related to current research in gravitation and quantum theory.
- Awareness of some current problems and new insights in gravitation and quantum theory.
- Conceptual understanding that enables the critical evaluation of current research, methodology or advanced scholarship.
- The ability to apply knowledge in the discipline to novel problems.
Students successfully completing the course should be able to:
- Apply complex concepts, methods and techniques to familiar and novel situations.
- Work with abstract concepts and in a context of generality.
- Reason logically and work analytically.
- Perform with high level of accuracy.
- Relate mathematical results to their physical applications.
- Transfer expertise between different topics in mathematical physics.
- Select and apply appropriate methods and techniques to solve problems.
- Justify conclusions using mathematical arguments with appropriate rigour.
- Communicate results using appropriate styles, conventions and terminology.
- Use appropriate IT packages effectively.
- Communicate with clarity.
- Work effectively, independently and under direction.
- Adopt effective strategies for study.